Answer:
x=5±√5, x=5-√5.
Step-by-step explanation:
Here's why:
First, keep the terms on the left-hand side and subtract 20 from both sides to get:
Original Equation: x²-10x+20=0
x²-10x+20-20=0-20
=x²-10x=-20
Next, use the property [b⋅1/2]². Notice that b is -10 in this case:
[b⋅1/2]²
=[-10⋅1/2]²
=25
Then, add the result, 25, to both sides of the equation in Step 1.
x²-10x+25=-20+25
Notice that the left side is a perfect square, so you can factor it out:
x²-10x+25=-20+25
=(x-5)²=-20+25
Combine like terms on the right-hand side:
(x-5)²=-20+25
=(x-5)²=5
Then, take the square root of both sides:
√(x-5)²=±√5
The square cancels out, which leaves you with:
x-5=±√5
Finally, isolate x by solving for the variable.
x-5=±√5
=x=5±√5
Therefore, your final answer is:
x=5±√5
When you are solving for other questions that involve completing the square, always remember to follow these steps, and you'll be good to go.
Hope this helped! :)
-Jina Wang
